What is resolution of vectors ?
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Hi,
Here is your answer,
RESOLUTION OF VECTORS
Any vector quantity can be represented as sum of two or three vectors which can be called components of vectors.
Example:- A body is projected obliquely with a velocity V ms⁻¹ at an angle 'θ' with horizontal plane it will travel in a parabolic path and then returns to plane. A part of the vectors acts along x-axis and another part acts along y-axis. Now, here we can say that 'x' component of velocity vector is responsible for displacement along x axis and y axis component of the vector is responsible for displacement along y-axis.
Now. have a look on the figure we can understand that Vx and Vy are horizontal and vertical component of the vector.
Vx = v cosθ ; Vy = v sinθ
If we have a vector in space we can also define 'z' component of the vector. For given set of axis a vector quantity can have maximum number of three components. Now, we can conclude that vector quantity can have infinite numbers of sets of rectangular components if we do pertain to a single set of axes.
If x is the magnitude in x direction ----> i to the power of n is the unit vector.
NOTE:- Further explanation is not required if you still need further explanation then do let me know. That will of higher order IIT mains. What i haven given is only based on CBSE Pattern Explanation.
Hope it helps you !
Here is your answer,
RESOLUTION OF VECTORS
Any vector quantity can be represented as sum of two or three vectors which can be called components of vectors.
Example:- A body is projected obliquely with a velocity V ms⁻¹ at an angle 'θ' with horizontal plane it will travel in a parabolic path and then returns to plane. A part of the vectors acts along x-axis and another part acts along y-axis. Now, here we can say that 'x' component of velocity vector is responsible for displacement along x axis and y axis component of the vector is responsible for displacement along y-axis.
Now. have a look on the figure we can understand that Vx and Vy are horizontal and vertical component of the vector.
Vx = v cosθ ; Vy = v sinθ
If we have a vector in space we can also define 'z' component of the vector. For given set of axis a vector quantity can have maximum number of three components. Now, we can conclude that vector quantity can have infinite numbers of sets of rectangular components if we do pertain to a single set of axes.
If x is the magnitude in x direction ----> i to the power of n is the unit vector.
NOTE:- Further explanation is not required if you still need further explanation then do let me know. That will of higher order IIT mains. What i haven given is only based on CBSE Pattern Explanation.
Hope it helps you !
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any vector quantity that can be represented as the sum of two or three vectors is indicated as resolution vector.
for example let a rocket travels at an angle of theta with th horizental of the earth surface.
this implies that the rocket makes an angle of theta with horizental plane and 90-theta with the vertical plane.
hence if we have to represent the motion of the rocket in vector form then we have to conside both the horizental factor and vertical factor.then their logical sum will be the required motion of the rocket which is known as the resolution vector
for example let a rocket travels at an angle of theta with th horizental of the earth surface.
this implies that the rocket makes an angle of theta with horizental plane and 90-theta with the vertical plane.
hence if we have to represent the motion of the rocket in vector form then we have to conside both the horizental factor and vertical factor.then their logical sum will be the required motion of the rocket which is known as the resolution vector
DebashishJoshi:
tnx
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